Decision Problems for Equational Theories of Relation Algebras

Decision Problems for Equational Theories of Relation Algebras
Author :
Publisher : American Mathematical Soc.
Total Pages : 148
Release :
ISBN-10 : 0821863274
ISBN-13 : 9780821863275
Rating : 4/5 (275 Downloads)

Book Synopsis Decision Problems for Equational Theories of Relation Algebras by : H. Andréka

Download or read book Decision Problems for Equational Theories of Relation Algebras written by H. Andréka and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. The provide researchers in algebra and logc with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.


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